The period of the function $f (x) =$$\frac{{|\sin x| + |\cos x|}}{{|\sin x - \cos x|}}$  is

Let $A = \{ {x_1},\,{x_2},\,............,{x_7}\} $ and $B = \{ {y_1},\,{y_2},\,{y_3}\} $ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f : A \to B$ that are onto, if there exist exactly three elements $x$ in $A$ such that $f(x)\, = y_2$, is equal to

Let $f : R -\{0,1\} \rightarrow R$ be a function such that $f(x)+f\left(\frac{1}{1-x}\right)=1+x$. Then $f(2)$ is equal to :

If $f(x)$ satisfies the relation $f\left( {\frac{{5x - 3y}}{2}} \right) = \frac{{5f(x) - 3f(y)}}{2}\forall x,y\, \in \,R$ and $f(0)=1, f'(0)=2$ then the period of $sin(f(x))$ is 

If $f(x)=\frac{\left(\tan 1^{\circ}\right) x+\log _{\varepsilon}(123)}{x \log _{\varepsilon}(1234)-\left(\tan 1^{\circ}\right)}, x > 0$, then the least value of $f(f(x))+f\left(f\left(\frac{4}{x}\right)\right)$ is $...........$.

Let $f$ be a real valued function defined by

$f(x) = sin^{-1} \left( {\frac{{\,\,1 - \,\,\left| x \right|}}{3}} \right) + cos^{-1}\left( {\frac{{\left| x \right|\,\, - \,\,3}}{5}} \right)$ .

Then domain of $f(x)$ is given by :